The distance around a circle---it's circumference---or the length of some portion thereof---a segment---is measured in linear distance units such as inches, centimeters, feet, or meters.
The portion of a circle (the relative distance around) that a segment represents---the segment's circular arc---is measured in units of angular magnitude. In basic geometry and lay usage, the most common angular unit is the degree. In scientific and higher math usage, the most common unit is the radian. The circumference of a circle has an arc of 360° (360 degrees), or 2π rad (2 × pi radians). A radian therefore is equivalent to 180/π degrees. Other units of angular magnitude include the turn (360° or 2π rad), grad (aka gon; 1/400 turn), quadrant (1/4 turn), arcminute (1/60°), and arcsecond (1/60 arcminute).
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There is no special unit related to the distance around a circle. It's a distance, a length measurement.Pick what fits. Millimeters, inches, yards, kilometers....It's possible to describe it in degrees too, referring to the width of an angle as seen from the center.Rarely used outside fairly specialized navigation purposes.
It was never confirmed. The degree was created as a unit equal to one three hundred sixtieth of the way around a circle
Since the radius of the unit circle is 1, the circumference is 2 x pi.
A 'unit cube'. Just like a circle with radius 1 and center at (0,0) is a 'unit circle'.
If x2 + y2 = 1, then the point (x,y) is a point on the unit circle.